(1) Field of the Invention
The present invention relates generally to a system and method for estimating the geodetic position of acoustic sensors, and more particularly to a system and method for estimating position which considers timing and sound velocity biases as parameters to be estimated, thus precluding biasing errors from propagating to the sensor coordinates.
(2) Description of the Prior Art
Underwater acoustic tracking ranges, as typically operated, utilize the well known principle of hyperbolic multilateration similar to radio frequency (RF) navigation systems. The accuracy and limitations of these systems has been well documented. The underwater acoustic environment, however, creates some unique differences. For example, both the RF and acoustic systems make timing measurements and convert them to range measurements. The nature of underwater acoustic wave propagation results in non-dispersive wave propagation, significantly smaller propagation velocities, shorter propagation distances, longer transit times and severe refraction through the stratified ocean. In addition, both types of tracking systems require precise knowledge of the relative and geodetic location of the reference sensors (transmitters and receivers). For a land based RF system, this is accomplished using well known, conventional terrestrial survey techniques. For a satellite based RF system, it requires techniques adapted for that environment. Historically, two methods have been employed for surveying underwater acoustic sensors, commonly referred to as the Vanderkulk and Spherical Least Squares methods, the main difference between the two methods being the use of geodetic position information for the acoustic sources. However, both techniques are extensions of the conventional, well known trilateration survey technique. A trilateration survey consists of making range measurements from reference points to points to be surveyed. The ranging measurements are obtained by making timing measurements and converting them to range measurements based upon a presumed knowledge of the propagation velocity of the transmitted acoustic signal. The major source of error for the traditional survey methods is systematic error or bias. This type of error can manifest itself both in the timing measurements and in the assumptions of the sound velocity. Timing biases are normally removed by making system timing measurements and removing the systematic component before processing, the systemantic component normally being a timing delay. Systematic errors in the acoustic propagation velocity, however, are more difficult to deal with because they cannot be measured and are generally functions of both space and time. For underwater acoustic multilateration tracking systems, the nature of the acoustic propagation is such that ray theory is considered valid. If one further restricts the propagation to direct monotonic acoustic ray paths, the propagation velocity is characterized by an Effective Sound Velocity (ESV). The ESV is that velocity which when multiplied by the transit time between two underwater points, yields the geometric or slant range between them. To avoid systematic (non-random) errors in the ESV calculation, an unbiased measurement for the Sound Speed Profile (SSP) is prerequisite. However, a typical measured SSP may have a 2 meter/second bias error. Consequently, the traditional methods may suffer significant errors on estimating the sensor coordinates.